ABSTRACT
L , then
du = 2π L
dx,
and the limits of integration are −L 2
to +L 2
instead of from −π to +π. Hence the Fourier
series expressed in terms of x is given by:
f (x) = a0 + ∞∑
[
an cos
( 2πnx
L
)
+ bn sin (
2πnx L
)]
where, in the range −L 2
to +L 2
:
and
a0 = 1L ∫ L
f (x) dx,
an = 2L ∫ L
f (x) cos (
2πnx L
)
dx
bn = 2L ∫ L
f (x) sin (
2πnx L
)
dx
The limits of integration may be replaced by any interval of length L, such as from 0 to L.
